Finite Group Databasebeta

← C53×#7829 #27215341

Subgroups — C53×#7829 #27215341

Order 13568.

394 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#2734C211yesmaximal, characteristic
2C53×#2100C212yesmaximal
3C53×#2095C211yesmaximal, characteristic
4C53×#1272C211yesmaximal, characteristic
5C53×#1271C212yesmaximal
6C2×C4⋊Q8×C53—21no—
7C2×#107×C53—21no—
8C2×#103×C53—21no—
9C53×#398—21no—
10C53×#395—22no—
11C53×#391C2211yescharacteristic
12C53×#389C2212yes—
13C53×#387—22no—
14C53×#384C2211yescharacteristic
15C53×#340—22no—
16C53×#340—22no—
17C53×#336C2211yescharacteristic
18C53×#336C2212yes—
19C22×Q8×C53—21no—
20C22×Q8×C53D411yescharacteristic
21C22×C8×C53—21no—
22C22×C8×C53—22no—
23C4⋊Q8×C53—42no—
24C4⋊Q8×C53—42no—
25C2×C4⋊C4×C53—22no—
26C2×C4⋊C4×C53—21no—
27C2×C4⋊C4×C53—22no—
28C2×C4⋊C4×C53—22no—
29C2×C4⋊C4×C53—21no—
30C2×C4⋊C4×C53D412yes—
31C2×C4⋊C4×C53D412yes—
32C2×C4⋊C4×C53D411yescharacteristic
33C2×C42×C53—21no—
34C2×C42×C53C2311yescharacteristic
35#107×C53—42no—
36#103×C53—42no—
37#95×C53—21no—
38#95×C53—22no—
39#95×C53—22no—
40#95×C53—22no—
41C2×Q8×C53—21no—
42C2×Q8×C53—42no—
43C2×Q8×C53—41no—
44C2×Q8×C53—41no—
45C2×Q8×C53—81no—
46C2×Q8×C53—81no—
47C2×Q8×C53SD1612yes—
48C22×C4×C53—22no—
49C22×C4×C53—21no—
50C22×C4×C53—21no—
51C22×C4×C53—22no—
52C22×C4×C53—41no—
53C22×C4×C53C2×D411yescharacteristic
54C22×C4×C53C2×D412yes—
55C2×C8×C53—22no—
56C2×C8×C53—41no—
57C2×C8×C53—41no—
58C2×C8×C53—42no—
59C2×C8×C53—42no—
60C2×C8×C53—42no—
61C4⋊C4×C53—22no—
62C4⋊C4×C53—44no—
63C4⋊C4×C53—41no—
64C4⋊C4×C53—42no—
65C4⋊C4×C53—41no—
66C4⋊C4×C53—41no—
67C4⋊C4×C53—44no—
68C4⋊C4×C53—42no—
69C4⋊C4×C53—42no—
70C4⋊C4×C53—81no—
71C4⋊C4×C53Q1614yes—
72C42×C53—41no—
73C42×C53—42no—
74C23×C53#12011yescharacteristic
75Q8×C53—42no—
76Q8×C53—81no—
77Q8×C53—84no—
78C2×C4×C53—21no—
79C2×C4×C53—22no—
80C2×C4×C53—21no—
81C2×C4×C53—22no—
82C2×C4×C53—22no—
83C2×C4×C53—24no—
84C2×C4×C53—42no—
85C2×C4×C53—41no—
86C2×C4×C53—42no—
87C2×C4×C53—41no—
88C2×C4×C53—42no—
89C2×C4×C53—42no—
90C2×C4×C53—41no—
91C2×C4×C53—42no—
92C2×C4×C53—42no—
93C2×C4×C53—81no—
94C2×C4×C53—82no—
95C2×C4×C53C2×SD1611yescharacteristic
96C2×C4×C53C2×Q1612yes—
97C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
98C2×C4×C53#13712yes—
99C8×C53—42no—
100C8×C53—82no—
101#7829C5311yesmaximal, characteristic, direct product factor, Sylow
102C22×C53#45011yescharacteristic
103C22×C53#45112yes—
104C22×C53#45311yescharacteristic
105C22×C53#45412yes—
106C22×C53#45811yescharacteristic
107C4×C53—21no—
108C4×C53—21no—
109C4×C53—22no—
110C4×C53—22no—
111C4×C53—42no—
112C4×C53—44no—
113C4×C53—82no—
114C4×C53—81no—
115C4×C53—161no—
116#2734C2×C5311yescharacteristic
117#2100C2×C5312yes—
118#2095C2×C5311yescharacteristic
119#1272C2×C5311yescharacteristic
120#1271C2×C5312yes—
121C2×C53#161311yescharacteristic
122C2×C53#161712yes—
123C2×C53#163311yescharacteristic
124C2×C53#163712yes—
125C2×C53#165711yescharacteristic
126C2×C4⋊Q8—21no—
127C2×#107—21no—
128C2×#103—21no—
129#398—21no—
130#395—22no—
131#391C22×C5311yescharacteristic
132#389C22×C5312yes—
133#387—22no—
134#384C22×C5311yescharacteristic
135#340—22no—
136#340—22no—
137#336C22×C5311yescharacteristic
138#336C22×C5312yes—
139C53#782911yescharacteristic, direct product factor, Sylow
140C22×Q8—21no—
141C22×Q8D4×C5311yescharacteristic
142C22×C8—21no—
143C22×C8—22no—
144C4⋊Q8—42no—
145C4⋊Q8—42no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4D4×C5312yes—
152C2×C4⋊C4D4×C5312yes—
153C2×C4⋊C4D4×C5311yescharacteristic
154C2×C42—21no—
155C2×C42C23×C5311yescharacteristic
156#107—42no—
157#103—42no—
158#95—21no—
159#95—22no—
160#95—22no—
161#95—22no—
162C2×Q8—21no—
163C2×Q8—42no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—81no—
167C2×Q8—81no—
168C2×Q8SD16×C5312yes—
169C22×C4—22no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—41no—
174C22×C4C2×D4×C5311yescharacteristic
175C22×C4C2×D4×C5312yes—
176C2×C8—22no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C4⋊C4—22no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C4⋊C4—44no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—44no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—81no—
192C4⋊C4Q16×C5314yes—
193C42—41no—
194C42—42no—
195C23#120×C5311yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—84no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—81no—
215C2×C4—82no—
216C2×C4C2×SD16×C5311yescharacteristic
217C2×C4C2×Q16×C5312yes—
218C2×C4AGL(1,ℤ/8)×C5311yescharacteristic
219C2×C4#137×C5312yes—
220C8—42no—
221C8—82no—
222C22C53×#45011yescharacteristic
223C22C53×#45112yes—
224C22C53×#45311yescharacteristic
225C22C53×#45412yes—
226C22C53×#45811yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—42no—
232C4—44no—
233C4—81no—
234C4—82no—
235C4—161no—
236C2C53×#161311yescharacteristic
237C2C53×#161712yes—
238C2C53×#163311yescharacteristic
239C2C53×#163712yes—
240C2C53×#165711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C53#120
commutator, Frattini, cosocleC2×C42C23×C53
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
101. #7829C53direct (N × H)
139. C53#7829direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C53×#27342
C53×#21002
C53×#20952
C53×#12722
C53×#12712
#782953